RL-bags: A conceptual, level-based approach to fuzzy bags

Parameters of Fuzzy Bags

“…For more details, see [2], [4]. In what follows, O is the set of all objects, and F (O) = {A|A : O → [0, 1]} is the set of all fuzzy subsets of O.…”

“…Then, they proposed new definitions for bags and fuzzy bags. As it is shown in [3], the lattice of all fuzzy bags defined by Delgado et al [2] is a complete Boolean algebra which is not compatible with the nature of fuzziness. Improving this incompatibility, in [4], we quoted a revised definition for fuzzy bags based on the proposed definition of bags in [2].…”

“…However, due to some existing drawbacks in the first definition of bags [1], the necessity of a revision of this notion revealed. The proposed definition by Delgado et al [2] has corrected these drawbacks. By some examples, they showed that the given definition for bags by Yager has some deficiencies and it was not well suited for representing and reasoning with real-world information.…”

On Algebraic Structure of L-Fuzzy Bags

“…The initial notion of bags, also called multisets, was introduced by Yager as an algebraic set‐like structure where an element can appear more than once. Different operations such as union, intersection, addition, and so on were defined and studied from an algebraic point of view . So far, several works have been done using this new concept; see Refs.…”

“…However, owing to some existing drawbacks in the first definition of bags, the necessity of a revision of this notion is obvious. The proposed definition by Delgado et al . has improved these drawbacks.…”